Question

Part A: Factor 2x2y2 + 6xy2 + 18x2y2. Show your work.

Part B: Factor x2 + 10x + 25. Show your work.

Part C: Factor x2 − 36. Show your work.

Answer 1

A.

`2xy^2(10x+3)`

B.

`(x+5)^2`

C.

`(x-6)(x+6)`

Explanation:

Part A. The expression
`2x^2y^2+6xy^2+18x^2y^2` consists of three terms:
`2x^2y^2,\ \ 6xy^2,\ \ 18x^2y^2` The first and the last terms are like terms, we can add them:

`2x^2y^2+18x^2y^2=20x^2y^2`

Now,

`20x^2y^2=2xy^2\cdot 10x\\ \\6xy^2=2xy^2\cdot 3`

So,

`2x^2y^2+6xy^2+18x^2y^2=2xy^2(10x+3)`

Part B. The expression
`x^2+10x+25` is a square of
`x+5,` so

`x^2+10x+25=(x+5)^2`

Part C. Use the difference of squares formula:

`x^2-36=x^2-6^2=(x-6)(x+6)`